摘要
Lions引入的变分形式中的渐近展开方法,用于线性问题是很有效的,但用于非线性问题,就会迂到很多麻烦,有时问题存在唯一,但找到解的渐近展开非常困难(见注记3.1).设Ω=Ω_0+?_1,在Ω_1上是线性算子,在Ω_0上是非线性算子,对有些问题可给出解的渐近展开算法.但在Ω_0和Ω_1上,同时是非线性算子时,直到现在仍是未解决的问题.设Ω=Ω_e+?_1(如图1)?=R^n。
Let Q= Q_0 + Q_1 be an open set in R^n. Consider a kind of nonlinear Neumannproblems: -Δu_0+α_1(x)u_0+α_2(x)|u_0|~su_0=f_0 in Q_0, (1) ε[-Δu_1+b(x)u_1]=f_1 in Q_1, u_0=u_1,(?u_?)/(?v)=ε(?u_1)/(?v) on s, (?u_0)/(?v)=g on Γ By using the Sobolev embedding theorem and the theory of monotone operators,an asymptotic expansion of the solution of (1) and the error estimate of this expa-nsion are given. Some open problems concerning problem (1) are proposed.
出处
《计算数学》
CSCD
北大核心
1989年第4期418-427,共10页
Mathematica Numerica Sinica
